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Some Approximate Solutions of Dyn01nic Problems in the Linear Theory of Thin Elastic Shells


Mortell, Michael Philip (1968) Some Approximate Solutions of Dyn01nic Problems in the Linear Theory of Thin Elastic Shells. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/11GT-4V56.


Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Knowles, James K.
Thesis Committee:
  • Unknown, Unknown
Defense Date:19 October 1967
Record Number:CaltechTHESIS:04052013-144005487
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7581
Deposited By: Benjamin Perez
Deposited On:05 Apr 2013 22:37
Last Modified:03 Apr 2024 23:43

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